Measurement of inclusive jet charged-particle fragmentation functions in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV with the ATLAS detector

EUROPEAN ORGANISATION FOR NUCLEAR RESEARCH (CERN)

CERN-PH-EP-2014-101

Submitted to: Physics Letters B

Measurement of inclusive jet charged-particle fragmentation

functions in Pb+Pb collisions at

√

s

N N

= 2.76

TeV with the

ATLAS detector

The ATLAS Collaboration

Abstract

Measurements of charged-particle fragmentation functions of jets produced in ultra-relativistic

nuclear collisions can provide insight into the modification of parton showers in the hot, dense medium

created in the collisions. ATLAS has measured jets in

√

s

N N

= 2.76

TeV Pb+Pb collisions at the LHC

using a data set recorded in 2011 with an integrated luminosity of 0.14 nb

−1

. Jets were reconstructed

using the anti-k

t

algorithm with distance parameter values R = 0.2, 0.3, and 0.4. Distributions of

charged-particle transverse momentum and longitudinal momentum fraction are reported for seven

bins in collision centrality for R = 0.4 jets with p

jet_T

> 100

GeV. Commensurate minimum p

T

values

are used for the other radii. Ratios of fragment distributions in each centrality bin to those measured

in the most peripheral bin are presented. These ratios show a reduction of fragment yield in central

collisions relative to peripheral collisions at intermediate z values, 0.04 . z . 0.2 and an enhancement

in fragment yield for z . 0.04. A smaller, less significant enhancement is observed at large z and large

p

T

in central collisions.

c

2014 CERN for the benefit of the ATLAS Collaboration.

Measurement of inclusive jet charged particle fragmentation functions in

Pb+Pb collisions at

√

s

NN

= 2.76 TeV with the ATLAS detector

The ATLAS Collaboration

Abstract

Measurements of charged-particle fragmentation functions of jets produced in ultra-relativistic nuclear col-lisions can provide insight into the modification of parton showers in the hot, dense medium created in the collisions. ATLAS has measured jets in√sNN= 2.76 TeV Pb+Pb collisions at the LHC using a data

set recorded in 2011 with an integrated luminosity of 0.14 nb−1. Jets were reconstructed using the anti-kt

algorithm with distance parameter values R = 0.2, 0.3, and 0.4. Distributions of charged-particle trans-verse momentum and longitudinal momentum fraction are reported for seven bins in collision centrality for R = 0.4 jets with pjet_T > 100 GeV. Commensurate minimum pT values are used for the other radii. Ratios

of fragment distributions in each centrality bin to those measured in the most peripheral bin are presented. These ratios show a reduction of fragment yield in central collisions relative to peripheral collisions at in-termediate z values, 0.04 . z . 0.2 and an enhancement in fragment yield for z . 0.04. A smaller, less significant enhancement is observed at large z and large pTin central collisions.

1. Introduction

Collisions between lead nuclei at the LHC are thought to produce a quark–gluon plasma (QGP), a form of strongly interacting matter in which quarks and gluons become locally deconfined. One predicted consequence of QGP formation is the “quenching” of jets generated in hard-scattering processes during the initial stages of the nuclear collisions [1]. Jet quenching refers, collectively, to a set of possible modifications of parton showers by the QGP through interactions of the constituents of the shower with the colour charges in the plasma [2, 3]. In particular, quarks and gluons in the shower may be elastically or inelastically scattered resulting in both deflection and energy loss of the constituents of the shower. The deflection and the extra radiation associated with inelastic processes may broaden the parton shower and eject partons out of an experimental jet cone [4–9]. As a result, jet quenching can potentially both soften the spec-trum of the momentum of hadrons inside the jet and reduce the total energy of the reconstructed jet. A complete characterization of the effects of jet quenching therefore requires measurements of both the single-jet suppression and the jet fragment dis-tributions.

Observations of modified dijet asymmetry dis-tributions [10–12], modified balance-jet transverse momentum (pT) distributions in γ+jet events [13],

and suppressed inclusive jet yield in Pb+Pb colli-sions at the LHC [14, 15] are consistent with the-oretical calculations of jet quenching. However, it has been argued that those measurements do not sufficiently discriminate between calculations that make different assumptions regarding the relative importance of the contributions described above [16]. Based on the above arguments, theoretical analyses are incomplete without experimental con-straints on the theoretical description of jet frag-ment distributions.

This Letter presents measurements of charged-particle jet fragmentation functions in √sNN =

2.76 TeV Pb+Pb collisions using 0.14 nb−1 of data recorded in 2011. The jets used in the measure-ments were reconstructed with the anti-kt[17]

algo-rithm using distance parameter values R = 0.2, 0.3, and 0.4. Results are presented for the charged-particle transverse momentum (~p_Tch) and longitu-dinal momentum fraction (z ≡ ~p_Tch· ~p_Tjet/|~p_Tjet|2₎

distributions, D(pT) ≡ 1 Njet dNch dpch T , (1)

D(z) ≡ 1 Njet

dNch

dz , (2)

of charged particles with pch

T > 2 GeV produced

within an angular range ∆R = 0.4 of the recon-structed jet directions for jets with pjet_T > 85, 92, and 100 GeV for R = 0.2, 0.3, and 0.4, respec-tively. Here, ∆R = p(∆φ)2_{+ (∆η)}2 _{where ∆φ}

(∆η) is the difference in azimuthal angles (pseudo-rapidities) between the charged particle and jet di-rections.1 _{The p}jet

T thresholds for the three R values

were chosen to match the R-dependence of the mea-sured transverse momentum of a typical jet. For simplicity, the terms “fragmentation functions” are used to describe the distributions defined in Eq. (2) with the understanding that D(z) is different from a theoretical fragmentation function, D(z, Q2), cal-culated using unquenched jet energies and with no restriction on the angles of particles with respect to the jet axis. Earlier measurements by CMS of jet fragmentation functions [18] in Pb+Pb collisions at the LHC show no significant modification, but the uncertainties on that measurement were not suffi-cient to exclude modifications at the level of ∼ 10%. CMS recently released a new result [19] using higher statistics data from 2011 that show fragmentation function modifications which are consistent with the results presented in this Letter.

2. Experimental setup

The measurements presented in this Letter were performed using the ATLAS calorimeter, inner de-tector, muon spectrometer, trigger, and data acqui-sition systems [20]. The ATLAS calorimeter sys-tem consists of a liquid argon (LAr) electromag-netic (EM) calorimeter covering |η| < 3.2, a steel– scintillator sampling hadronic calorimeter covering |η| < 1.7, a LAr hadronic calorimeter covering 1.5 < |η| < 3.2, and two LAr forward calorimeters (FCal) covering 3.2 < |η| < 4.9. The hadronic calorime-ter has three sampling layers longitudinal in shower depth and has a ∆η ×∆φ granularity of 0.1×0.1 for |η| < 2.5 and 0.2 × 0.2 for 2.5 < |η| < 4.9.2 _{The EM}

1 _{ATLAS uses a right-handed coordinate system with its}

origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y axis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2).

2_{An exception is the third sampling layer that has a}

seg-mentation of 0.2 × 0.1 up to |η| = 1.4.

calorimeters are segmented longitudinally in shower depth into three compartments with an additional pre-sampler layer. The EM calorimeter has a gran-ularity that varies with layer and pseudorapidity, but which is generally much finer than that of the hadronic calorimeter. The middle sampling layer, which typically has the largest energy deposit in EM showers, has a granularity of 0.025 × 0.025 over |η| < 2.5.

The inner detector [21] measures charged parti-cles within the pseudorapidity interval |η| < 2.5 using a combination of silicon pixel detectors, sili-con microstrip detectors (SCT), and a straw-tube transition radiation tracker (TRT), all immersed in a 2 T axial magnetic field. All three detectors are composed of a barrel and two symmetrically placed end-cap sections. The pixel detector is com-posed of 3 layers of sensors with nominal feature size 50 µm × 400 µm. The SCT barrel section contains 4 layers of modules with 80 µm pitch sensors on both sides, while each end-cap consists of nine layers of double-sided modules with radial strips having a mean pitch of 80 µm. The two sides of each SCT layer in both the barrel and the end-caps have a rel-ative stereo angle of 40 mrad. The TRT contains up to 73 (160) layers of staggered straws interleaved with fibres in the barrel (end-cap). Charged parti-cles with pch

T & 0.5 GeV typically traverse three

layers of pixel sensors, four layers of double-sided SCT sensors, and, in the case of |η| < 2.0, 36 TRT straws.

Minimum bias Pb+Pb collisions were identified using measurements from the zero degree calorime-ters (ZDCs) and the minimum-bias trigger scin-tillator (MBTS) counters [20]. The ZDCs are lo-cated symmetrically at z = ±140 m and cover |η| > 8.3. In Pb+Pb collisions the ZDCs mea-sure primarily “spectator” neutrons, which origi-nate from the incident nuclei and do not interact hadronically. The MBTS detects charged particles over 2.1 < |η| < 3.9 using two counters placed at z = ±3.6 m. MBTS counters are divided into 16 modules with 8 different positions in azimuth and covering 2 different |η| intervals. Each counter pro-vides measurement of both the pulse heights and arrival times of ionization energy deposits.

Events used in this analysis were selected for recording by a combination of Level-1 minimum-bias and High Level Trigger (HLT) jet triggers. The Level-1 trigger required a total transverse en-ergy measured in the calorimeter of greater than 10 GeV. The HLT jet trigger ran the offline Pb+Pb

jet reconstruction algorithm, described below, for R = 0.2 jets except for the application of the final hadronic energy scale correction. The HLT trig-ger selected events containing an R = 0.2 jet with transverse energy ET> 20 GeV.

3. Event selection and data sets

This analysis uses a total integrated luminosity of 0.14 nb−1 of Pb+Pb collisions recorded by ATLAS in 2011. Events selected by the HLT jet trigger were required to have a reconstructed primary ver-tex and a time difference between hits in the two sides of the MBTS detector of less than 3 ns. The primary vertices were reconstructed from charged-particle tracks with pch

T > 0.5 GeV. The tracks were

reconstructed from hits in the inner detector us-ing the ATLAS track reconstruction algorithm de-scribed in Ref. [22] with settings optimized for the high hit density in heavy-ion collisions [23]. A total of 14.2 million events passed the described selec-tions.

The centrality of Pb+Pb collisions was charac-terized by ΣE_TFCal, the total transverse energy mea-sured in the forward calorimeters [23]. Jet fragmen-tation functions were measured in seven central-ity bins defined according to successive percentiles of the ΣEFCal

T distribution ordered from the most

central to the most peripheral collisions: 0–10%, 10–20%, 20–30%, 30–40%, 40–50%, 50–60%, and 60–80%. The percentiles were defined after correct-ing the ΣEFCal

T distribution for a 2% minimum-bias

trigger inefficiency that affects the most peripheral events which are not included in this analysis.

The performance of the ATLAS detector and of-fline analysis in measuring jets and charged par-ticles in the environment of Pb+Pb collisions was evaluated using a large Monte Carlo (MC) event sample obtained by overlaying simulated [24] PYTHIA [25] pp hard-scattering events at √s = 2.76 TeV onto 1.2 million minimum-bias Pb+Pb events recorded in 2011. The same number of PYTHIA events was produced for each of five in-tervals of ˆpT, the transverse momentum of outgoing

partons in the 2 → 2 hard-scattering, with bound-aries 17, 35, 70, 140, 280, and 560 GeV. The detector response to the PYTHIA events was simulated us-ing Geant4 [26], and the simulated hits were com-bined with the data from the minimum-bias Pb+Pb events to produce 1.2 million overlaid events for each ˆpTinterval.

4. Jet and charged-particle analysis

Charged particles included in the fragmentation measurements were required to have at least two hits in the pixel detector, including a hit in the first pixel layer if the track trajectory makes such a hit expected, and seven hits in the silicon mi-crostrip detector. In addition, the transverse (d0)

and longitudinal (z0sin θ) impact parameters of

the tracks measured with respect to the primary vertex were required to satisfy |d0/σd0| < 3 and

|z0sin θ/σz| < 3, where σd0and σzare uncertainties

on d0 and z0sin θ, respectively, obtained from the

track-fit covariance matrix. Jets were reconstructed using the techniques described in Ref. [14], which are briefly summarized here.

The anti-kt algorithm was first run in

four-momentum recombination mode, on ∆η × ∆φ = 0.1 × 0.1 logical towers and for three values of the anti-kt distance parameter, R = 0.2, 0.3, and 0.4.

The tower kinematics were obtained by summing electromagnetic-scale energies of calorimeter cells within the tower boundaries. Then, an iterative procedure was used to estimate a layer- and η-dependent underlying event (UE) energy density while excluding actual jets from that estimate. The UE energy was subtracted from each calorimeter cell within the towers included in the reconstructed jet. The correction takes into acount a cos 2φ mod-ulation of the calorimeter response due to elliptic flow of the medium [23] which is estimated by mea-surement of the amplitude of that modulation in the calorimeter. The final jet kinematics were cal-culated via a four-momentum sum of all (assumed massless) cells contained within the jets using sub-tracted ETvalues. A correction was applied to the

reconstructed jet to account for jets not excluded or only partially excluded from the UE estimate. Then, a final jet η- and ET-dependent hadronic

en-ergy scale calibration factor was applied.

After the reconstruction, additional selections were applied for the purposes of this analysis. “UE jets” generated by fluctuations in the underlying event, were removed using techniques described in Ref. [14].

To prevent neighbouring jets from distorting the measurement of the fragmentation functions, jets were required to be isolated. The isolation cut re-quired that there be no other jet within ∆R = 1 having pT > pisoT where p

iso

T , the isolation

thresh-old, is set to half of the analysis threshold for each R value, piso_T = 42.5, 46, and 50 GeV for R = 0.2, 0.3,

Njet Cut description 0–10% 60–80% All jets 41191 2579 UE jet rejection 41116 2570 Isolation 40986 2554 Muon rejection 40525 2523 Inactive area exclusion 39548 2458 Trigger jet match 39548 2458 Table 1: Number of jets for two centrality bins in data as a function of the selection criteria applied. Each line specifies the number of jets passing all cuts for the given line and above.

and 0.4, respectively. To prevent muons from semileptonic heavy-flavour decays from influencing the measured fragmentation functions, all jets with reconstructed muons having pT > 4 GeV within a

cone of size ∆R = 0.4 were excluded from the anal-ysis. To prevent inactive regions in the calorime-ters from producing artificial high z fragments, jets were required to have more than 90% of their en-ergy contained within fully functional regions of the calorimeter. Finally, all jets included in the analy-sis were required to match HLT jets reconstructed with transverse momenta greater than the trigger threshold of 20 GeV. The HLT jets were found to be fully efficient for the jet kinematic selection used in this analysis. Table 1 shows the impact of the cuts on the number of measured jets in central (0–10%) and peripheral (60–80%) collisions. All these cuts together retain more than 96% of all jets.

5. Jet and track reconstruction performance The performance of the ATLAS detector and analysis procedures in measuring jets was evaluated from the MC sample using the procedures described in Ref. [14]. Reconstructed MC jets were matched to “truth” jets obtained by separately running the anti-ktalgorithm on the final-state PYTHIA

parti-cles3 _{for the three jet R values used in this}

analy-sis. For the jet fragmentation measurements, the most important aspect of the jet performance is the jet energy resolution (JER). For jet energies & 100 GeV, the JER in central (0–10%) collisions for R = 0.4 jets has comparable contributions from

3 _{Final-state PYTHIA particles are defined as all}

gener-ated particles with lifetimes longer than 0.3·10−10_s

originat-ing from the primary interaction or from subsequent decay of particles with shorter lifetimes.

UE fluctuations and “intrinsic” resolution of the calorimetric jet measurement. For peripheral col-lisions and R = 0.2 jets, the intrinsic calorimeter resolution dominates the JER. The value of JER evaluated for jets with pT= 100 GeV in 0–10%

col-lisions is 0.18, 0.15, and 0.13 for R = 0.4, R = 0.3, and R = 0.2 jets, respectively.

The combination of the finite JER and the steeply falling jet pT spectrum produces a net

mi-gration of jets from lower pT to higher pT values

(hereafter referred to as “upfeeding”) such that a jet reconstructed with a given pTjetreccorresponds, on

average, to a lower truth-jet pT, hpTjettruei. The

rela-tionship between hpT jet

truei and pTjetrec was evaluated

from the MC data set for the different centrality bins and three R values used in this analysis. For the jet pTjetrec values used in this analysis, that

rela-tionship is well described by a linear dependence, hpTjettruei = αpTjetrec+ β. (3)

Sample values for α and β and the resulting hpTjettruei

values for R = 0.2 and R = 0.4 jets in peripheral and central collisions are listed in Table 2. The extracted relationships between pTjetrec and hpTjettruei

will be used in the fragmentation analysis to correct for the average shift in the measured jet energy.

MC studies indicate that the efficiency for PYTHIA jets to be reconstructed and to pass UE jet rejection exceeds 98% for pjet_T > 60 GeV in the 0–10% centrality bin. For kinematic selection of jets used in this study, the jet reconstruction was fully efficient.

The efficiency for reconstructing charged par-ticles within jets in Pb+Pb collisions was evalu-ated using the MC sample. Fig. 1 shows com-parisons of distributions of four important track-quality variables between data and MC simulation for reconstructed tracks over a narrow pch_T interval, 5 < pch

T < 7 GeV, to minimize the impact of

dif-ferences in MC and data charged-particle pch T

dis-tributions. The ratios of the data to MC distribu-tions also shown in the figure indicate better than 1% agreement in the η dependence of the average number of pixel and SCT hits associated with the tracks. The distributions of d0and z0sin θ agree to

. 10% except in the tails of the distributions, which contribute a negligible fraction of the distribution. For the purpose of evaluating the track reconstruc-tion performance and for the evaluareconstruc-tion of response matrices that are used in the unfolding (described below), the reference “truth” particles were taken

Centrality Jet R α β (GeV) hpTjettruei(100 GeV)

0–10% 0.2 0.995 ± 0.003 −7.6 ± 0.5 91.9 GeV 60–80% 0.2 0.989 ± 0.002 −6.0 ± 0.3 92.9 GeV 0–10% 0.4 1.027 ± 0.004 −17.7 ± 0.5 85.0 GeV 60–80% 0.4 0.964 ± 0.002 −2.3 ± 0.2 94.1 GeV

Table 2: The relationship between the mean truth-jet transverse momenta, hpTjettruei, and corresponding reconstructed jet

transverse momenta, pTjetrec. Sample values of α and β obtained from linear fits to hpTjettruei(pTjetrec) (see text) according to

Eq. (3) and the resulting hpTjettruei for pTjetrec= 100 GeV.

<Pixel Hits> 0 1 2 3 4 5 6 7 < 7 GeV trk T 5 < p Data 2011 MC 2011 ATLAS -1 =2.76 TeV, 0.14 nb NN s Pb+Pb η -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Data/MC 0.95 1 1.05 < S C T H it s > 0 2 4 6 8 10 12 14 ATLAS -1 =2.76 TeV, 0.14 nb NN s Pb+Pb η -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Data/MC 0.95 1 1.05 trk N/N -5 10 -4 10 -3 10 -2 10 -1 10 1 10 ATLAS -1 =2.76 TeV, 0.14 nb NN s Pb+Pb [mm] 0 d -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Data/MC 0.5 1 1.5 trk N/N -5 10 -4 10 -3 10 -2 10 -1 10 1 ATLAS -1 =2.76 TeV, 0.14 nb NN s Pb+Pb [mm] θ sin 0 z -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Data/MC 0.5 1 1.5

Figure 1: Comparison between data and MC distributions for four different charged-particle reconstruction selection parameters. The distributions are shown for the 0–10% cen-trality bin and for charged-particle transverse momenta in the range 5 < pch

T < 7 GeV. Top: average number of pixel

(left) and SCT (right) hits per track. Bottom: distribution of track impact parameters with respect to the reconstructed primary vertex; both transverse, d0(left), and longitudinal,

z0sin θ (right), impact parameters are shown. Ratios of

dis-tributions in data to those in MC simulation are shown for each quantity.

from the set of final-state PYTHIA charged parti-cles. These were matched to reconstructed charged particles using associations between detector hits and truth tracks recorded by the ATLAS Geant4 simulations. Truth particles for which no matching reconstructed particle was found were considered lost due to inefficiency.

The charged-particle reconstruction efficiency, ε(pT, η), was evaluated separately in each of the

seven centrality bins used in this analysis for truth particles within ∆R = 0.4 of R = 0.4 truth jets hav-ing pT

jet

true> 100 GeV. Fig. 2 shows the efficiency as

a function of truth-particle pTaveraged over |η| < 1

(top) and 1 < |η| < 2.5 (bottom) for the 0–10% and 60–80% centrality bins. For pT < 8 GeV, ε(pT, η)

was directly evaluated using fine bins in pT and

η. For pT > 8 GeV the pT dependence of the

effi-ciencies were parameterized separately in the two pseudorapidity intervals shown in Fig. 2 using a functional form that describes trends at low pT as

well as at high pT. An example of the resulting

parameterizations is shown by the solid curves in Fig. 2. A centrality-dependent systematic uncer-tainty in the parameterized efficiencies, shown by the shaded bands in Fig. 2, was evaluated based on both the uncertainties in the parameterization and on observed variations of the efficiency with pT,

which largely result from loss of hits in the SCT at higher detector occupancy. Thus, the systematic uncertainty in the 60–80% centrality bin is small because no significant variation of the efficiency is observed at low detector occupancy, while the un-certainties are largest for the 0–10% centrality bin with the largest detector occupancies.

The efficiencies shown in Fig. 2 decrease by about 12% between the |η| < 1 interval covered by the SCT barrel and the 1 < |η| < 2.5 interval covered primarily by the SCT end-cap. More significant localized drops in efficiency of about 20% are ob-served over 1 < |η| < 1.2 and 2.3 < |η| < 2.5 corre-sponding to the transition between the SCT barrel and end-cap and the detector edge respectively. To account for this and other localized variations of the high pTreconstruction efficiency with

pseudorapid-ity, the parameterizations in Fig. 2 for pT> 8 GeV

are multiplied by an η-dependent factor evaluated in intervals of 0.1 units to produce ε(pT, η).

[GeV] true T p 10 2 10 E ff ic ie n c y 0.5 0.6 0.7 0.8 0.9 1 0-10% 60-80% 0-10% parameterization 60-80% parameterization ATLAS Simulation =2.76 TeV NN s Pb+Pb PYTHIA + Data | < 1.0 η | [GeV] true T p 10 2 10 E ff ic ie n c y 0.4 0.5 0.6 0.7 0.8 0.9 0-10% 60-80% 0-10% parameterization 60-80% parameterization ATLAS Simulation =2.76 TeV NN s Pb+Pb PYTHIA + Data | < 2.5 η 1.0 < |

Figure 2: Charged-particle reconstruction efficiency as a function of truth pT, for 0–10% (red) and 60–80% (blue)

centrality bins in the region |η| < 1 (top) and 1 < |η| < 2.5 (bottom). The pT values for the 0–10% points are shifted

for clarity. The solid curves show parameterizations of effi-ciencies. The shaded bands show the systematic uncertainty in the parameterized efficiencies (see text).

6. Fragmentation functions and unfolding Jets used for the fragmentation measurements presented here were required to have pjet_T > 85, 92 and 100 GeVfor R = 0.2, 0.3, and 0.4 jets, re-spectively. The jet thresholds for R = 0.3 and R = 0.2 jets represent the typical energy measured with the smaller jet radii for an R = 0.4 jet with pT = 100 GeV. Jets were also required to have

ei-ther 0 < |η| < 1 or 1.2 < |η| < 1.9. The restric-tion of the measurement to |η| < 1.9 avoids the region at the detector edge with reduced efficiency (|η| > 2.3). The exclusion of the range 1 < |η| < 1.2 removes from the measurement jets whose large-z fragments, which are typically collinear with the jet axis, would be detected in the lower-efficiency η region spanning the gap between SCT barrel and end-cap. While this exclusion does not significantly change the result of the measurement, it reduces the systematic uncertainties at large z or pch

T.

The fragmentation functions were measured for charged particles with pch_T > 2 GeV within an an-gular range ∆R = 0.4 of the jet direction for all three R values used in the jet reconstruction. To

re-duce the effects of the UE broadening of the jet po-sition measurement, for R = 0.3 and R = 0.4 jets, the jet direction was taken from that of the closest matching R = 0.2 jet within ∆R = 0.3 when such a matching jet was found. For each charged parti-cle, the longitudinal jet momentum fraction, z, was calculated according to

z = p

ch T

pjet_T cos ∆R, (4) where ∆R here represents the angle between the charged particle and jet directions.4

Charged particles from the UE contribute a pch_T -and centrality-dependent background to the mea-surement that must be subtracted to obtain the true fragmentation functions. The contribution of the UE background was separately evaluated for R = 0.2, 0.3, and 0.4 jets in events having at least one such jet above the jet pT thresholds using a

grid of ∆R = 0.4 cones that spanned the full cov-erage of the inner detector. Any such cone having a charged particle with pch

T > 6 GeV was assumed

to be associated with a real jet in the event and was excluded from the UE background determina-tion. The threshold of 6 GeV was chosen to be high enough to avoid bias of the UE pch

T distribution.

The resulting per-jet UE charged-particle yields, dnUE_ch/dpch_T were evaluated over 2 < pch_T < 6 GeV as a function of pch_T, pjet_T, and ηjet, averaged over all cones in all events within a given centrality bin according to: dnUE ch dpch_T = 1 Ncone ∆Ncone ch (p ch T, p jet T , η jet₎ ∆pch_T . (5) Here Ncone represents the number of background

cones having a jet of a given radius above the cor-responding pjet_T threshold, and ∆N_chcone represents the number of charged particles in a given pch

T bin

in all such cones evaluated for jets with a given pjet_T and ηjet_{. Not shown in Eq. (5) is a correction}

fac-tor that was applied to each background cone to correct for the difference in the average UE-particle yield at a given pch

T between the η position of the

cone and ηjet_{, and a separate correction factor to}

account for the difference in the elliptic flow mod-ulation at the φ position of the UE cone and φjet. That correction was based on a parameterization

4_{The ∆R is a boost-invariant replacement for the polar}

z D(z) -2 10 -1 10 1 10 2 10 3 10 10 × 0-10% Raw 10 × 0-10% Unfolded 60-80% Raw 60-80% Unfolded ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb R = 0.4 T anti-k z -1 10 1 Raw/Unfolded 0.6 0.81 1.2 1.4 1.6 1.82 2.2 2.4 0-10% + 1 60-80% z 0-10% / 60-80% 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Raw Unfolded ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb R = 0.4 T anti-k z -1 10 1 Raw/Unfolded 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 _z 0-10% / 60-80% 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Raw Unfolded ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb R = 0.2 T anti-k z -1 10 1 Raw/Unfolded 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Figure 3: Measured and unfolded D(z) distributions for R = 0.4 and R = 0.2 jets in central (0–10%) and peripheral (60–80%) collisions. Top left: R = 0.4 Dmeas_{(z) and D(z) distributions, bottom left: ratios of measured to unfolded R = 0.4 D(z)}

distributions with the 0–10% shifted by +1 for clarity. Top middle and right: central-to-peripheral ratios of measured (Rmeas D(z))

and unfolded (RD(z)) distributions for R = 0.4 and R = 0.2, respectively. Bottom middle and right: ratio of RD(z)measto RD(z)

for R = 0.4 and R = 0.2, respectively.

of the pch

T and centrality dependence of previously

measured elliptic flow coefficients, v2 [23].

By evaluating the UE contribution only from events containing jets included in the analysis, the background automatically has the correct distribu-tion of centralities within a given centrality bin. The dnUE_ch/dpch_T is observed to be independent of pjet_T both in the data and MC simulation. That ob-servation excludes the possibility that the upfeeding of jets in pjet_T due to the finite JER could induce a dependence of the UE on jet pT. However, such

upfeeding was observed to induce in the MC events a pjet_T-independent, but centrality-dependent mis-match between the extracted dnUE

ch/dpchT and the

actual UE contribution to reconstructed jets. That mismatch was found to result from intrinsic corre-lations between the charged-particle density in the UE and the MC pjet_T error, ∆pjet_T = pTjetrec− pTjettrue.

In particular, jets with positive (negative) ∆pjet_T are found to have an UE contribution larger (smaller) than jets with ∆pjet_T ∼ 0. Due to the net up-feeding on the falling jet spectrum, the selection of jets above a given pjet_T threshold causes the UE contribution to be larger than that estimated from the above-described procedure. The average frac-tional mismatch in the estimated UE background was found to be independent of pch

T and to vary

with centrality by factors between 1.04-1.08, 1.07-1.10, and 1.12-1.15 for R = 0.2, 0.3, and 0.4, respec-tively. The measured dnUE_ch/dpch_T values in the data

were corrected by these same factors before being subtracted.

Two different sets of charged-particle fragmenta-tion distribufragmenta-tions were measured for each centrality bin and R value:

Dmeas(pT) ≡ 1 ε  ₁ Njet ∆Nch ∆pch_T − dnUE ch dpT  , (6) and Dmeas(z) ≡1 ε 1 Njet ∆Nch ∆z − dnUE_ch dpT    _pch T =zp jet T ! , (7) where Njetrepresents the total number of jets

pass-ing the above-described selection cuts in a given centrality bin, and ∆Nch represents the number of

measured charged particles within ∆R = 0.4 of the jets in given bins of pch

T and z, respectively.

The efficiency correction, 1/ε, was applied on a per-particle basis using the parameterized MC ef-ficiency, ε(pT, η), assuming pTchtrue = pTchrec. While

that assumption is not strictly valid, the efficiency varies sufficiently slowly with pTchtrue that the error

introduced by this assumption is . 1% everywhere. The measured Dmeas_{(z) distributions for R = 0.4}

jets in the 0–10% and 60–80% centrality bins are shown in the top left panel in Fig. 3. The top middle panel shows the ratio of Dmeas(z) between central (0–10%) and peripheral (60–80%) collisions, Rmeas_D(z) ≡ Dmeas_(z)|

0−10/Dmeas(z)|60−80. For

T p )_T D(p -3 10 -2 10 -1 10 1 10 10 × 0-10% Raw 10 × 0-10% Unfolded 60-80% Raw 60-80% Unfolded ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb R = 0.4 T anti-k [GeV/c] T p 10 102 Raw/Unfolded 0.6 0.81 1.2 1.4 1.6 1.82 2.2 2.4 0-10% + 1 60-80% [GeV/c] T p 0-10% / 60-80% 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Raw Unfolded ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb R = 0.4 T anti-k [GeV/c] T p 10 102 Raw/Unfolded 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 [GeV/c] T p 0-10% / 60-80% 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Raw Unfolded ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb R = 0.2 T anti-k [GeV/c] T p 10 102 Raw/Unfolded 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Figure 4: Measured and unfolded D(pT) distributions for R = 0.4 and R = 0.2 jets in central (0–10%) and peripheral (60–80%)

collisions. Top left: R = 0.4 Dmeas_(p

T) and D(pT) distributions, bottom left: ratios of measured to unfolded R = 0.4 D(pT)

distributions with the 0–10% shifted by +1 for clarity. Top middle and right: central-to-peripheral ratios of measured (Rmeas D(pT))

and unfolded (RD(pT)) distributions for R = 0.4 and R = 0.2, respectively. Bottom middle and right: ratio of R

meas

D(pT)to RD(pT)

for R = 0.4 and R = 0.2, respectively.

right panel for R = 0.2 jets. Similar plots are shown in Fig. 4 but for Dmeas_(p

T). The Dmeas(z)

ra-tios for both R = 0.2 and R = 0.4 indicate an en-hanced fragment yield at low z, z . 0.04, in jets in the 0–10% centrality bin compared to jets in the 60–80% centrality bin and a suppressed yield of fragments with z ∼ 0.1. Similar results are observed in the Dmeas(pT) ratios over the

corre-sponding pTranges. The R = 0.2 Dmeas(z) and the

R = 0.2 and R = 0.4 Dmeas_(p

T) ratios rise above

one for z & 0.2 or pT& 25 GeV. However, the ratios

differ from one by only 1–2σ(stat). No such varia-tions of the Dmeas_{(z) and D}meas_(p

T) distributions

with centrality as seen in the data are observed in the MC simulation. The central-to-peripheral ra-tios of MC Dmeas_{(z) and D}meas_(p

T) distributions

for R = 0.4 and R = 0.2 jets (not shown) are within 3% of one for all z and pT.

The Dmeas_(p

T) and Dmeas(z) distributions were

unfolded using a one-dimensional Singular Value Decomposition (SVD) method [27] implemented in RooUnfold [28] to remove the effects of charged par-ticle and jet pT resolution. The SVD method

im-plements a regularized matrix-based unfolding that attempts to “invert” the equation b = Ax, where x, is a true spectrum, b is an observed spectrum, and A is the “response matrix” that describes the transformation of x to b. For D(pT), the unfolding

accounts only for the charged-particle pT

resolu-tion and uses a response matrix derived from the

MC data set that describes the distribution of re-constructed pch

T as a function of MC truth pchT. The

response matrix A(pTchrec, pTchtrue) is filled using the

procedures described in Section 5. The D(z) un-folding simultaneously accounts for both charged particle and jet resolution using a response ma-trix A(zrec, ztrue) with ztrue (zrec) calculated us-ing purely truth (fully reconstructed) quantities. A cross-check was performed for the D(z) unfold-ing that included only the jet energy resolution to ensure that the combination of the two sources of resolution in the one-dimensional unfolding did not distort the result. Because the Dmeas_{(z) and}

Dmeas_(p

T) distributions were already corrected for

the charged-particle reconstruction efficiency, the response matrices were only populated with truth particles for which a reconstructed particle was ob-tained and each entry was corrected for reconstruc-tion efficiency so as to not distort the shape of the true distributions.

To ensure that statistical fluctuations in the MC pTjettrue or ztrue distributions do not distort the

un-folding, those distributions were smoothed by fit-ting them to appropriate functional forms. The truth D(pT) distributions were fit to polynomials in

ln(pT). The truth D(z) distributions were

parame-terized using an extension of a standard functional form [29],

where a, b, c, diwere free parameters of the fit. The

non-standard additional parameter “c” was added to improve the description of the truth distribution at large z. When filling the truth spectra and re-sponse matrices, the entries were weighted to match the truth spectra to the fit functions.

The SVD unfolding was performed using a reg-ularization parameter obtained from the ninth sin-gular value (k = 9) of the unfolding matrix. Sys-tematic uncertainties in the unfolding due to reg-ularization were evaluated by varying k over the range 5–12 for which the unfolding was observed to be neither significantly biased by regularization nor unstable. The statistical uncertainties in the unfolded spectra were obtained using the pseudo-experiment method [27]. The largest absolute un-certainty obtained over 5 ≤ k ≤ 12 was taken to be the statistical uncertainty in the unfolded result.

Unfolded fragmentation functions, D(z), are shown in the top left panel in Fig. 3 and com-pared to the corresponding Dmeas_{(z) distributions}

for R = 0.4 jets in central (0–10%) and peripheral (60–80%) collisions. Similar results for D(pT) are

shown in Fig. 4. For both figures, the ratios of un-folded to measured distributions are shown in the bottom left panel with the ratio for 0–10% central-ity bin offset by +1. Those ratios show that the unfolding has minimal impact on the fragmentation functions in both peripheral and central collisions. Only the largest z point in the 0–10% bin changes by more than 20%.

The middle and top right panels in Fig. 3 (Fig. 4) show for R = 0.4 and R = 0.2 jets, respec-tively the ratios of unfolded D(z) (D(pT))

distri-butions, RD(z)≡ D(z)|0−10/D(z)|60−80 (RD(pT)≡

D(pT)|0−10/D(pT)|60−80), compared to the ratios

before unfolding. The unfolding reduces the D(z) ratio slightly at low z but otherwise leaves the shapes unchanged. To evaluate the impact of the unfolding on the difference between central and pe-ripheral fragmentation functions, the middle and bottom right panels in Fig. 3 (Fig. 4) show the ra-tio of Rmeas

D(z)(R meas

D(pT)) to RD(z)(RD(pT)). Except for

the lowest z point, the ratio is consistent with one over the entire z range. Thus, the features observed in Rmeas_D(z)(R_D(pmeas

T)), namely the enhancement at low

z (pT) in central collisions relative to peripheral

col-lisions, the suppression at intermediate z (pT), and

the rise above one at large z (pT) are robust with

respect to the effects of the charged particle and jet pT resolution.

7. Systematic uncertainties

Systematic uncertainties in the unfolded D(z) and D(pT) distributions can arise due to

uncertain-ties in the jet energy scale and jet energy resolu-tion, from systematic uncertainties in the unfolding procedure including uncertainties in the shape of the truth distributions, uncertainties in the charged particle reconstruction, and from the UE subtrac-tion procedure.

The systematic uncertainty due to the jet en-ergy scale (JES) has two contributions, an absolute JES uncertainty and an uncertainty in the varia-tion of the JES from peripheral to more central collisions. The absolute JES uncertainty was de-termined by shifting the transverse momentum of the reconstructed jets according to the evaluation of the jet energy scale uncertainty in Ref. [30]. The typical size of the JES uncertainty for jets used in this study is 2%. The shift in the JES has neg-ligible impact on the ratios between central and peripheral events of D(pT) and D(z) distributions

whereas it has a clear impact on the D(pT) and

D(z) distributions. At high pT or z the

result-ing uncertainty reaches 15%. The evaluation of centrality-dependent uncertainty on JES uses the estimates from Ref. [14]. The centrality-dependent JES uncertainty is largest for the most central col-lisions where it reaches 1.5%. The evaluation of the jet energy resolution (JER) uncertainty follows the procedure applied in proton–proton jet mea-surements [31]. The typical size of JER uncertainty for jets used in the study is less than 2%. This uncertainty is centrality independent since the di-jets in MC are overlayed to real data. The result-ing combined systematic uncertainty from JER and centrality-dependent JES on the ratios reaches 6% at high pT and 10% at high z and it has a similar

size in the case of D(pT) or D(z) distributions as

in the case of their ratios.

The systematic uncertainty associated with the unfolding is connected with the sensitivity of the unfolding procedure to the choice of regularization parameter and to the parameterization of the truth distribution. The uncertainty due to the choice of regularization parameter was evaluated by varying k over the range 5–12. The typical systematic un-certainty is found to be smaller than 3% or 2% for the D(z) or D(pT), respectively. The

system-atic uncertainty due to the parameterization of the truth distribution was determined from the statis-tical uncertainties of the fits to these distributions.

This systematic uncertainty is below 1% or 2% for the D(z) or D(pT), respectively.

The estimate of systematic uncertainty due to the tracking efficiency follows methods of the in-clusive charged particle measurement [23]. The un-certainty is quantified using the error of the fit of tracking efficiency and by varying the tracking se-lection criteria. In the intermediate-pT region the

systematic uncertainty is less than 2%. In the low and high pT region the systematic uncertainty is

larger, but less than 8%.

An independent evaluation of potential system-atic uncertainties in the central-to-peripheral ra-tios of D(z) and D(pT), due to all aspects of the

analysis, was obtained by evaluating the deviation from unity of the MC central (0–10%) to periph-eral (60–80%) ratios of the fragmentation functions. Since there is no jet quenching employed in MC simulation, the ratios are expected not to show any deviation from unity. No deviation from unity is indeed observed, the largest localized deviation is . 4%. To quantify the deviations from unity, the MC RD(z)and RD(pT) ratios were fit by

piece-wise continuous functions composed of linear func-tions defined over the z (pT) ranges z=0.02–0.06

(pT=2–6 GeV), z=0.06–0.3 (pT=6–30 GeV), and

z > 0.3 (pT > 30 GeV) with parameters

con-strained such that the linear functions match at the boundaries. The resulting fits are used as esti-mates of the systematic uncertainties on all mea-sured RD(z) and RD(pT) ratios reported in

Sec-tion 8. This systematic uncertainty is certainly cor-related with and may overlap with other systematic uncertainties described above.

8. Results

The unfolded fragmentation functions, D(z) and D(pT), for R = 0.4 jets are shown in Fig. 5 for

the seven centrality bins included in the analysis with the distributions for different centralities mul-tiplied by successive values of two for presentation purposes. The shaded error bands indicate system-atic uncertainties as discussed in the previous sec-tion. The D(pT) and D(z) distributions have

sim-ilar shapes that are characteristic of fragmentation functions with a steep drop at the endpoint.

To evaluate the centrality dependence of the frag-mentation functions, ratios were calculated of the R = 0.4 D(z) distributions for all centrality bins ex-cluding the peripheral bin to the D(z) measured in the peripheral, 60–80% centrality bin. The results

are shown in Fig. 6. The ratios for all centralities show an enhanced yield of low z fragments and a suppressed yield of fragments at intermediate z val-ues in more central collisions relative to the 60–80% centrality bin. For the 0–10% centrality bin, the yield of fragments at z = 0.02 is enhanced rela-tive to that in the 60–80% centrality bin by 25% while the yield at z = 0.1 is suppressed by about 10%. The size of the observed modifications at low, intermediate, and high z decreases gradually from central to peripheral collisions.

The statistical and systematic uncertainties on RD(z)grow as z → 1 due to the statistical

fluctua-tions on the D(z) distribufluctua-tions at large z and due to the sensitivity of the steeply falling D(z) distri-butions to JER and JES systematic uncertainties. The results in Fig. 6 show central values for RD(z)

above one at high z for the 0–10% through the 30–40% centrality bins but the RD(z) values differ

from one by typically 1σ(stat). Fig. 7 shows ratios of R = 0.4 D(pT) distributions from non-peripheral

centrality bins to those in the peripheral, 60–80% centrality bin. The ratios in the figure show the same features as the D(z) ratios, namely an en-hancement at low pT, a suppression at intermediate

pT, and an increase above one at large pT that is

more significant than that seen for D(z). The mag-nitudes of the deviations from one in the D(z) and D(pT) ratios are similar in the low, intermediate,

and high z and pTregions. This demonstrates that

the modifications observed in Fig. 6 do not result from distortions of the z measurement due to JER and JES.

To further demonstrate that the centrality-dependent modifications observed in D(z) and D(pT) do not result from unknown UE effects not

included in the systematic uncertainties, Fig. 8 shows ratios of D(z) and D(pT) distributions

be-tween central (0–10%) and peripheral (60–80%) col-lisions for R = 0.2 and R = 0.3 jets. The fluctua-tions in the UE are a factor of approximately 100% (30%) smaller for R = 0.2 (R = 0.3) jets than they are for R = 0.4 jets. Nonetheless, the features seen in the R = 0.4 D(z) or D(pT) ratios are also present

in the R = 0.2 and R = 0.3 ratios with the same magnitudes. Due to the reduced systematic uncer-tainties on D(z) and D(pT) for R = 0.2 and R = 0.3

jets compared to R = 0.4 jets, the enhancement in the fragmentation functions at large z or pTin

cen-tral collisions is more significant for the smaller jet sizes.

z -1 10 1 D(z) -2 10 -1 10 1 10 2 10 3 10 4 10 6

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Figure 5: Unfolded R = 0.4 longitudinal charged particle fragmentation function, D(z) and the charged particle transverse momentum distribution, D(pT), for the seven centrality bins included in this analysis. The statistical uncertainties are

ev-erywhere smaller than the points. The yellow shaded error bars indicate systematic uncertainties. Grey lines connecting the central values of distributions are to guide the eye.

Centrality z=0.02–0.04 z=0.04–0.2 z=0.4–1.0 R ∆D(z)dz R z∆D(z)dz R ∆D(z)dz R z∆D(z)dz R ∆D(z)dz R z∆D(z)dz 0-10% 0.79+0.19_−0.25 0.020+0.005_−0.007 −1.7+0.6 −0.8 −0.14 +0.04 −0.06 0.06 +0.05 −0.04 0.033 +0.026 −0.021 10-20% 0.66+0.17_−0.18 0.016+0.005_−0.005 −1.6+0.7 −0.8 −0.12+0.05−0.06 0.05+0.05−0.04 0.029+0.026−0.021 20-30% 0.52+0.13_−0.18 0.013+0.004_−0.005 −1.3+0.6 −0.6 −0.12 +0.04 −0.04 0.04 +0.04 −0.04 0.025 +0.024 −0.020 30-40% 0.39+0.12_−0.17 0.009+0.004_−0.005 −1.3+0.6 −0.7 −0.10+0.04−0.05 0.06+0.04−0.04 0.036+0.020−0.019 40-50% 0.38+0.11_−0.15 0.009+0.003_−0.004 −0.6+0.6 −0.8 −0.07 +0.04 −0.06 −0.01 +0.04 −0.04 −0.005 +0.024 −0.021 50-60% 0.28+0.15_−0.21 0.006+0.004_−0.006 −1.2+0.9 −0.7 −0.08+0.06−0.06 0.04+0.04−0.04 0.025+0.021−0.021

Table 3: Differences of D(z) distributions in different centralities with respect to peripheral events for R = 0.3 jets. The errors represent combined statistical and systematic uncertainties.

z -1 10 1 D(z) R 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 0-10%/60-80% >100 GeV jet T p R=0.4 T anti-k ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb z -1 10 1 D(z) R 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 30-40%/60-80% ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb z -1 10 1 D(z) R 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 Data Systematic Uncertainty 10-20%/60-80% ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb z -1 10 1 D(z) R 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 40-50%/60-80% ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb z -1 10 1 D(z) R 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 20-30%/60-80% ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb z -1 10 1 D(z) R 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 50-60%/60-80% ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb

Figure 6: Ratios of D(z) for six bins in collision centrality to those in peripheral (60–80%) collisions, D(z)|cent/D(z)|60−80,

for R = 0.4 jets. The error bars on the data points indicate statistical uncertainties while the yellow shaded bands indicate systematic uncertainties. [GeV] T p 10 102 )_T D(p R 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 0-10%/60-80% >100 GeV jet T p R=0.4 T anti-k ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb [GeV] T p 10 102 )_T D(p R 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 30-40%/60-80% ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb [GeV] T p 10 102 )_T D(p R 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 Data Systematic Uncertainty 10-20%/60-80% ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb [GeV] T p 10 102 )_T D(p R 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 40-50%/60-80% ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb [GeV] T p 10 102 )_T D(p R 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 20-30%/60-80% ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb [GeV] T p 10 102 )_T D(p R 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 50-60%/60-80% ATLAS =2.76 TeV NN s Pb+Pb -1 0.14 nb

Figure 7: Ratios of unfolded D(pT) distributions for six bins in collision centrality to those in peripheral (60–80%) collisions,

D(pT)|cent/D(pT)|60−80, for R = 0.4 jets. The error bars on the data points indicate statistical uncertainties while the yellow

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Figure 8: Ratios of unfolded fragmentation functions, D(z) (top) and D(pT) (bottom), for central (0–10%) collisions to those

in peripheral (60–80%) collisions for R = 0.2 (left) and R = 0.3 (right) jets. The fragmentation functions were evaluated using charged hadrons within ∆R = 0.4 of the jet axis. The error bars on the data points indicate statistical uncertainties while the yellow shaded bands indicate systematic uncertainties.

Centrality z=0.02–0.04 z=0.04–0.2 z=0.4–1.0 R ∆D(z)dz R z∆D(z)dz R ∆D(z)dz R z∆D(z)dz R ∆D(z)dz R z∆D(z)dz 0-10% 0.65+0.21_−0.20 0.017+0.006_−0.005 −1.7_−0.6+0.5 −0.14+0.04_−0.05 0.07+0.05_−0.04 0.037+0.030_−0.022 10-20% 0.60+0.16_−0.16 0.016+0.005_−0.004 −1.6+0.7 −0.7 −0.12 +0.05 −0.05 0.08 +0.05 −0.04 0.046 +0.029 −0.025 20-30% 0.48+0.11_−0.14 0.013+0.003_−0.004 −1.6_−0.5+0.6 −0.13+0.04_−0.04 0.04+0.05_−0.04 0.026+0.029_−0.024 30-40% 0.44+0.11_−0.15 0.011+0.003_−0.004 −1.4+0.6 −0.7 −0.11 +0.05 −0.05 0.07 +0.04 −0.05 0.044 +0.021 −0.028 40-50% 0.33+0.09_−0.14 0.009+0.003_−0.004 −1.0_−0.8+0.6 −0.09+0.04_−0.06 −0.03+0.05_−0.04 −0.011+0.030_−0.020 50-60% 0.27+0.12_−0.18 0.007+0.003_−0.005 −1.0+0.8 −0.7 −0.07 +0.06 −0.06 0.04 +0.04 −0.05 0.027 +0.024 −0.029

Table 4: Differences of D(z) distributions in different centralities with respect to peripheral events for R = 0.2 jets. The errors represent combined statistical and systematic uncertainties.

9. Discussion

To quantify the effects of the modifications ob-served in Fig. 8 on the actual distribution of frag-ments within the measured jets, the differences in fragmentation functions, ∆D(z) = D(z)|cent−

D(z)|60−80 were calculated and integrals of these

distributions,R ∆D(z)dz taken over three z ranges chosen to match the observations: 0.02–0.04, 0.04– 0.2, and 0.4–1. The last interval was chosen to focus on the region where RD(z) > 1. The

re-sults are given in Table 3 and Table 4 for R = 0.3 and R = 0.2 jets, respectively. Similar results were obtained for R = 0.4 jets but with larger uncer-tainties. The results presented in the tables indi-cate an increase in the number of particles with 0.02 < z < 0.04 of less than one particle per jet in the 0–10% centrality bin relative to the 60–80% centrality bin. A decrease of about 1.5 particles per jet is observed for 0.04 < z < 0.2. The differences between the integrals of the fragmentation func-tions over 0.4 < z < 1 are not significant relative to the uncertainties. The results forR ∆D(z)dz shown in the two tables indicate that in the most central collisions a small fraction, < 2%, of the jet trans-verse momentum is carried by the excess particles in 0.02 < z < 0.04 for central collisions, but that the depletion in fragment yield in 0.04 < z < 0.2 accounts on average for about 14% of pjet_T.

To better evaluate the significance of the in-crease in RD(z) and RD(pT) above one at large z

or pT, average RD(z)and RD(pT)ratios were

calcu-lated by summing the central and peripheral D(z) or D(pT) distributions over different regions

corre-sponding to the last n points in the measured distri-butions, n = 2 − 6. For each resulting average ratio,

RD(z) or RD(pT), the significance of the deviation

from one was evaluated as (RD(z)− 1)/σ(RD(z))

or (RD(pT)− 1)/σ(RD(pT)) where σ represents the

combined statistical and systematic uncertainty. Because there is significant cancellation of system-atic uncertainties in the ratios, this analysis pro-vides a more sensitive evaluation of the significance of the large-z excess. For R = 0.4 jets the combined RD(z)(RD(pT)), differs from one by approximately

1σ (1.5σ) for any of the n values. For R = 0.2 jets, RD(z) differs from 1 by approximately 1.5σ for all

n values, while RD(pT) differs from one by 2σ for

n = 3–6 corresponding to pT> 47.5 GeV through

pT> 20 GeV. The greater significance of the

devia-tions of the R = 0.2 RD(pT)relative to the R = 0.2

RD(z)and the R = 0.4 RD(z)and RD(pT)can be

at-tributed to the reduced role of the jet energy resolu-tion in influencing the measurement of the central-to-peripheral ratios for large hadron momenta.

Theoretical predictions for medium modifications of fragmentation functions based on radiative en-ergy loss [32–35] have generally predicted substan-tial reduction in the yield of high pT, or large-z

fragments and an enhancement at low pT or low

z. The predicted reduction at large z generically results from the radiative energy loss of the lead-ing partons in the shower and the resultlead-ing redis-tribution of the jet energy to lower z hadrons. In-stead of a reduction, an enhanced yield of high z fragments is seen in the data. However, the differ-ence between observed behaviour at large z and ex-pectations from theoretical calculations may be at least partially attributed to the fact that the frag-mentation functions presented in this paper were evaluated with respect to the energies of quenched

jets. In contrast, theoretical analyses of the frag-mentation functions of quenched jets are typically evaluated in terms of the initial, unquenched jet energies. However, some recent theoretical anal-yses [36, 37] of jet fragmentation functions using quenched jet energies have shown that jet quench-ing calculations can reproduce the general features observed in the results presented in this Letter. In addition to direct modifications of the fragmenta-tion funcfragmenta-tion due to quenching, the quenching may indirectly alter the fragmentation function of inclu-sive jets by altering the relative fraction of quarks and gluons.

The simultaneous effects of quenching on the hadron constituents of jets and the measured jet energies may explain a relative increase of experi-mental fragmentation functions in central collisions at large z as suggested by the data. Jets that frag-ment to large-z hadrons may lose less energy than typical jets due to reduced formation or colour-neutralization time [38]. Thus, the fragmentation function measured for inclusive jets may have a higher proportion of jets with large-z hadrons. The results in Ref. [36] indicate such an effect that is qualitatively similar to the data.

10. Conclusions

This Letter has presented measurements by ATLAS of charged-particle fragmentation functions in jets produced in√sNN= 2.76 TeV Pb+Pb

col-lisions at the LHC. The measurements were per-formed using a data set recorded in 2011 with an integrated luminosity of 0.14 nb−1. Jets were re-constructed with the anti-ktalgorithm for distance

parameters R = 0.2, 0.3, and 0.4, and the contribu-tions of the underlying event to the jet kinemat-ics and the jet fragment distributions were sub-tracted. Jet fragments were measured within an angular range ∆R = 0.4 from the jet axes for all three jet sizes. Distributions of per-jet charged-particle transverse momentum, D(pT), and

longitu-dinal momentum fraction, D(z), were presented for seven bins in collision centrality for jet pT> 85, 92,

and 100 GeV, respectively, for R = 0.2, R = 0.3, and R = 0.4 jets. Ratios of fragmentation functions in the different centrality bins to the 60–80% bin were presented and used to evaluate the medium modifications of jet fragmentation. Those ratios show an enhancement in fragment yield in central collisions for z . 0.04, a reduction in fragment yield

for 0.04 . z . 0.2 and an enhancement in the frag-ment yield for z > 0.4. The modifications decrease monotonically with decreasing collision centrality from 0–10% to 50–60%. A similar set of modifi-cations is observed in the D(pT) distributions over

corresponding pTranges.

Acknowledgements

We thank CERN for the very successful opera-tion of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.

We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbai-jan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CON-ICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF, DNSRC and Lundbeck Foundation, Denmark; EPLANET, ERC and NSRF, European Union; IN2P3-CNRS, CEA-DSM/IRFU, France; GNSF, Georgia; BMBF, DFG, HGF, MPG and AvH Foundation, Germany; GSRT and NSRF, Greece; ISF, MINERVA, GIF, I-CORE and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO, Netherlands; BRF and RCN, Norway; MNiSW and NCN, Poland; GRICES and FCT, Portugal; MNE/IFA, Romania; MES of Russia and ROSATOM, Russian Federation; JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and MIZˇS, Slove-nia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of Bern and Geneva, Switzer-land; NSC, Taiwan; TAEK, Turkey; STFC, the Royal Society and Leverhulme Trust, United King-dom; DOE and NSF, United States of America.

The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN and the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Ger-many), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 facilities worldwide.

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